New sampling formulae related to linear canonical transform
New sampling formulae related to linear canonical transform
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与线性正则变换相关的新采样公式
DOI：
10.1016/j.sigpro.2006.09.008
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发表时间：
2007-05-01
影响因子：
4.4
通讯作者：
Wang, Yue
中科院分区：
文献类型：
--
作者：
Li, Bing-Zhao;Tao, Ran;Wang, Yue
线性正则变换（LCT）是具有四个参数a、B、c、d的积分变换，并且已经被证明是光学、雷达系统分析、滤波器设计、相位恢复、模式识别和许多其他应用的有力工具。许多著名的变换，如傅里叶变换、分数傅里叶变换和菲涅耳变换，都可以看作是线性正则变换的特例。本文提出了一种新的采样公式，用于重构线性正则变换意义下的带限或时限信号。首先，以简单的方法导出了带限信号的采样定理。然后，基于傅里叶变换与线性正则变换之间的关系，得到了另外两个新的采样公式，即以一半奈奎斯特速率从信号及其一阶导数或广义Hilbert变换中获取样本。著名的傅立叶域或分数傅立叶域中的采样定理被证明是所取得的结果的特殊情况。最后给出了实验结果，验证了所得结果的准确性.最后，讨论了这些新结果和未来的工作相关的线性正则变换。(c)2006 Elsevier B.V.保留所有权利。
Linear canonical transform (LCT) is an integral transform with four parameters a, b, c, d and has been shown to be a powerful tool for optics, radar system analysis, filter design, phase retrieval, pattern recognition, and many other applications. Many well-known transforms such as the Fourier transform, the fractional Fourier transform, and the Fresnel transform can be seen as special cases of the linear canonical transform. In this paper, new sampling formulae for reconstructing signals that are band-limited or time-limited in the linear canonical transform sense have been proposed. Firstly, the sampling theorem representation of band-limited signals associated with linear canonical transform from the samples taken at Nyquist rate is derived in a simple way. Then, based on the relationship between the Fourier transform and the linear canonical transform, the other two new sampling formulae using samples taken at half the Nyquist rate from the signal and its first derivative or its generalized Hilbert transform are obtained. The well-known sampling theorems in Fourier domain or fractional Fourier domain are shown to be special cases of the achieved results. The experimental results are also proposed to verify the accuracy of the obtained results. Finally, discussions about these new results and future works related to the linear canonical transform are proposed. (c) 2006 Elsevier B.V. All rights reserved.